The least integral value $\alpha$ of $x$ such that $\frac{x - 5}{x^2 + 5x - 14} > 0$ satisfies:

Let $a$ and $b$ be two positive real numbers such that $a+2b \leq 1$. Let $A_1$ and $A_2$ be respectively the areas of circles with radii $ab^3$ and $b^2$. Then,the maximum possible value of $\frac{A_1}{A_2}$ is

The feasible region represented by the inequations $2x + 3y \leq 18$,$x + y \geq 10$,$x \geq 0$,$y \geq 0$ is

In an experiment,a solution of hydrochloric acid is to be kept between $30^{\circ} \text{C}$ and $35^{\circ} \text{C}$. What is the range of temperature in degree Fahrenheit if the conversion formula is given by $C = \frac{5}{9}(F - 32)$,where $C$ and $F$ represent temperature in degree Celsius and degree Fahrenheit,respectively?

Solve for $x$ in the following inequality: $\frac{4}{x+1} \leq 3 \leq \frac{6}{x+1}$ where $x > 0$.

The number of elements in the set $S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \leq 0 \text{ and } x^2 - 3x > 0\}$ is